After the thorough investigation and comparison, I finally decided to choose Mathematica as my companion in course study and scientific research. Looking back at the time I spent with it, there were a lot of colorful memories, exciting and frustrating, inspring and puzzling. But what is certain is that learning Mathematica and exploring the world of science with it was truly a fascinating experience, and I strongly recommend that you give it a try.

    The first time I found Mathematica to be helpful in my studies was one year ago, when I was learning Calculus III. As you know, Calculus III in Tsinghua is one of the fundamental mathematical courses for all engineering students. It mainly deals with multivariate calculus and differential equations, which gave me a perfect opportunity to use Mathematica! I still remember when Professor Tan Zeguang was teaching multivariate calculus, he excitedly utilized Mathematica in class to illustrate abstract concepts and three dimensional figures that are hard to visualize. Some of my works using Mathematica in Calculus III are shown below.

    This is a 3D plot showing the underlying spatial relationship of a question in the final examination, which I plotted after the exam and used it to successfully confirm my answer.

    This is a snapshot of a piece of script I wrote to solve a problem in spatial analytic geometry. Although this kind of problems could well be solved by hand, Mathematica provided me with a clearer and more accurate way to do so. I often use Mathematica to check my solutions and I can always gain a better understanding and even discover new findings from the results.

    I had not thought that Mathematica could be applied to courses like Principle of Machinery before I gave it a try. There was a chapter concerning the mechanism and applications of gears in this course, which was quite puzzling for me. So I tried to use Mathematica to create some intuitive illustrations of different kinds of gears and their structure, which turned out to be really helpful! Here is an example showing the mechanism of a specific kind of gear called an involute gear. It was the first time that I had used the powerful Manipulate function in Mathematica.

    The single function Manipulate gives immediate access to a huge range of powerful interactive capabilities. For any expression with symbolic parameters, Manipulate automatically creates an interface for manipulating the parameters. Manipulate supports not only mouse and keyboard manipulation, but also gamepads and other devices.

    Ever since I first experienced the benefit Mathematica brought to me, I had been seeking help from it whenever the opportunity arose. The following is an example where I used Mathematica to conduct a statistical experiment in my Probability and Statistics course.

    And the following is part of my experimentation assignment in Simulation and Modeling course this semester; I used Mathematica to finish the whole assignment, including both the core statistical analysis and the formatting of the documentation.

    The most successful and meaningful utilization of Mathematica happened at the beginning of this semester, when I participated in the Mathematical Contest in Modeling. I used Mathematica to analyze the large amount of data provided by the problem and to visualize the data according to our solution requirements. Mathematica’s capability and flexibility in dealing with various kinds of data and its strong data visualization capabilities contributed greatly to our success in the competition. Here are some diagrams in our final report of the contest, which were all drawn by Mathematica with some basic functions plus flexible control of the function parameters.

    In this semester, my Mathematica skills in using Packages have greatly improved. One of the most important features of Mathematica is that it is an extensible system. There is a certain amount of mathematical and other functionality that is built into Mathematica. But by using the Mathematica language, it is always possible to add more functionality. For many kinds of calculations, what is built into the standard version of Mathematica will be quite sufficient. However, if you work in a particular specialized area, you may find that you often need to use certain functions that are not built into Mathematica. In such cases, you may well be able to find a Mathematica package that contains the functions you need, or try to write your own packages based on the requirement. Mathematica packages are files written in the Mathematica language. They consist of collections of Mathematica definitions which "teach" Mathematica about particular application areas.

    At first, I was motivated to write a package on my own by the course assignment of Engineering Economy, which deals with compounding interest. We students are required to frequently calculate compounding-interest related problems using various kinds of formulae. With my package, solving problems in related chapters in Engineering Economy becomes quick and convenient. During this task-oriented learning process, I have generally grasped the method and technique in Package Development using Mathematica. I then wrote a package for the course Operations Research II, which deals with continuous time Markov chain and implements the CTMC uniformization algorithms.

    I shared my packages with all my classmates and had some discussion with them on topics of both the professional knowledge and Mathematica technology. It turns out that writing packages on my own not only satisfies my curiosity and interest in such fields, but also helps us to conveniently solve real-life professional problems. I am now really enjoying this way of learning: finding problems while studying, learning Mathematica to search for help, solving the problems and improving my Mathematica skills at the same time.

    Learning and exploring with Mathematica is a motivating studying style, and my experience confirms the old saying: The best way to learn is to use.

(To be continued…)